Copies of c0(Γ) in the space of bounded linear operators

The space L ( X , Y ) stands for the Banach space of all bounded linear operators from X to Y endowed with the operator norm. It is shown that c 0 ( Γ ) embeds into L ( X , Y ) if and only if l ∞ ( Γ ) embeds into L ( X , Y ) or c 0 ( Γ ) embeds into Y . As a consequence, we extend a classical Kalto...

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Bibliographic Details
Published inArchiv der Mathematik Vol. 112; no. 6; pp. 623 - 631
Main Authors Pérez, Sergio A., Rincón-Villamizar, Michael A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2019
Subjects
Mathematics
Mathematics and Statistics
46E15
Secondary 46E40
Primary 46B03
Embeddings of
Spaces of bounded linear operators
46B25
spaces
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Summary:The space L ( X , Y ) stands for the Banach space of all bounded linear operators from X to Y endowed with the operator norm. It is shown that c 0 ( Γ ) embeds into L ( X , Y ) if and only if l ∞ ( Γ ) embeds into L ( X , Y ) or c 0 ( Γ ) embeds into Y . As a consequence, we extend a classical Kalton theorem by proving that if c 0 ( Γ ) embeds into L ( X , Y ) and X has the | Γ | -Josefson–Nissenzweig property, then l ∞ ( Γ ) also embeds into L ( X , Y ) . We also show that, for certain Banach spaces X and Y , c 0 ( Γ ) embeds complementably into L ( X , Y ) if and only if c 0 ( Γ ) embeds into Y .
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-018-01296-0